Theoretical study of the reactions of AlF with HCl: Reaction pathways

The mechanisms for the reactions of AlF with HCl have been characterized in detail using DFT as well as the ab initio method, including zero-point corrections. From the potential energy profile it can be predicted that the reaction process of forming the new Al(III) hydride HAlFCl compound for this reaction is spontaneous with a low activation energy barrier. The reaction yielding to AlFCl₂ and molecular hydrogen was calculated to be highly exothermic. The present calculations also show that the possible routes to the trihalides species start more favorable with the primary insertion products.     

Syntheses, structures, and photophysical properties of mono- and dinuclear sulfur-rich gold(I) complexes

The dinuclear gold complexes [{Au(PPh 3)} 2(mu- dmid)] ( 1) ( dmid = 1,3-dithiole-2-one-4,5-dithiolate) and [{Au(PPh 3)} 2(mu- dddt)] ( 2) ( dddt = 5,6-dihydro-1,4-dithiine-2,3-dithiolate) were synthesized and characterized by X-ray crystallography. Both complexes exhibit intramolecular aurophilic interactions with Au...Au distances of 3.1984(10) A for 1 and 3.1295(11) A for 2. A self-assembly reaction between 4,5-bis(2-hydroxyethylthio)-1,3-dithiole-2-thione ( (HOCH 2 CH 2 ) 2 dmit) and [AuCl(tht)] affords the complex [AuCl{ (HOCH 2 CH 2 ) 2 dmit}] 2 ( 4), which possesses an antiparallel dimeric arrangement resulting from a short aurophilic contact of 3.078(6) A. This motif is extended into two dimensions due to intra- and intermolecular hydrogen bonds via the hydroxyethyl groups, giving rise to a supramolecular network. Three compounds were investigated for their rich photophysical properties at 298 and 77 K in 2-MeTHF and in the solid state; [Au 2(mu- dmid)(PPh 3) 2] ( 1), [Au 2(mu- dddt)(PPh 3) 2] ( 2), and [AuCl{( HOCH 2 CH 2 ) 2 dmit}] ( 4). 1 exhibits relatively long-lived LMCT (ligand-to-metal charge transfer) emissions at 298 K in solution (370 nm; tau e approximately 17 ns, where M is a single gold not interacting with the other gold atom; i.e., the fluxional C-SAuPPh 3 units are away from each other) and in the solid state (410 nm; tau e approximately 70 mus). At 77 K, a new emission band is observed at 685 nm (tau e = 132 mus) and assigned to a LMCT emission where M is representative for two gold atoms interacting together consistent with the presence of Au...Au contacts as found in the crystal structure. In solution at 77 K, the LMCT emission is also red-shifted to 550 nm (tau e approximately 139 mus). It is believed to be associated to a given rotamer. 2 also exhibits LMCT emissions at 380 nm at 298 K in solution and at 470 nm in the solid state. 4 exhibits X/MLCT emission (halide/metal to ligand charge transfer) where M is a dimer in the solid state with obvious Au...Au interactions, resulting in red-shifted emission band, and is a monomer in solution in the 10 (-5) M concentration (i.e., no Au...Au interactions) resulting in blue-shifted luminescence. Both fluorescence and phosphorescence are observed for 4.     

Integration formulas via the Fenchel subdifferential of nonconvex functions

Starting from explicit expressions for the subdifferential of the conjugate function, we establish in the Banach space setting some integration results for the so-called epi-pointed functions. These results use the ε-subdifferential and the Fenchel subdifferential of an appropriate weak lower semicontinuous (lsc) envelope of the initial function. We apply these integration results to the construction of the lsc convex envelope either in terms of the ε-subdifferential of the nominal function or of the subdifferential of its weak lsc envelope.     

Controllability and strong controllability of differential inclusions

In this paper, we prove sufficient conditions for controllability and strong controllability in terms of the Mordukhovich subdifferential for two classes of differential inclusions. The first one is the class of sub-Lipschitz multivalued functions introduced by Loewen-Rockafellar (1994) [10]. The second one, introduced recently by Clarke (2005) [18], is the class of multivalued functions which are pseudo-Lipschitz and satisfy the so-called tempered growth condition. To do this, we establish an error bound result in terms of the Mordukhovich subdifferential outside Asplund spaces.     

Organic thin films based on a dicyanovinyl-quaterthiophene: Influence of electrode configuration on third-order nonlinear optical properties measured by electroabsorption spectroscopy

Electroabsorption (EA) studies at room temperature on organic thin films based on a dicyanovinyl-quaterthiophene 4T-V(CN)₂ are reported. An electric field modulation is applied to the samples for two different electrode geometries, i.e. sandwich and coplanar versus the organic layer. Changes in optical absorption coefficient of 4T-V(CN)₂ based thin films are measured and analyzed to determine the character of the optical transition in the visible range (400-800 nm). Depending on the experimental electrode configuration, magnitude of electroabsorption responses are different, possibly due to different distribution of the externally applied electric field. The results indicate a higher resolution of EA response for the sandwich electrode configuration and confirm the charge transfer exciton character of 4T-V(CN)₂ in contrast to the unsubstituted quaterthiophene 4T. Finally, a third-order nonlinear susceptibility χ⁽³⁾ (−ω; ω, 0, 0) of 16 × 10⁻¹² e.s.u. is obtained.     

Tangency conditions for multivalued mappings

We prove that interiority conditions imply tangency conditions for two multivalued mappings from a topological space into a normed vector space. As a consequence, we obtain the lower semicontinuity of the intersection of two multivalued mappings. An application to the epi-upper semicontinuity of the sum of convex vector-valued mappings is given.     

Preface to “Optimization,Convex and Variational Analysis”

Set-Valued and Variational Analysis -     

Interdiffusion/reaction at the polymer/polymer interface in multilayer systems probed by linear viscoelasticity coupled to FTIR and NMR measurements

This paper describes the experimental investigation of the interdiffusion/reaction mechanisms of asymmetric polymer-polymer interfaces. The study deals with the assessment of the chemical reactions occurring at the interface between two reactive polymers. A focal point of the investigation was to study these interfacial reactions by an array of techniques at very different space scales: from macroscopic viscoelastic investigations to IR and NMR spectroscopies at the molecular scale. The studied material pairs include PE-GMA/PA6 as the reactive system (RS) and PE/PA6 as the non-reactive one (NRS) - of coextruded multilayer polymers, i.e., after processing. The linear viscoelastic properties of the reactive multilayer systems were determined and the mechanisms were analyzed by NMR and FTIR measurements. Substantial reactions occurred during the rheological measurements and the results indicated the preferential formation of a copolymer at the interface, triggered by the neighboring layers. Moreover, the contribution of an interface/interphase effect was investigated along with the increase in the number of layers. The results showed that the variation in dynamic modulus of the multilayer system was a result of both diffusion and chemical reaction. Specific experiments were carried out to follow-up on the physicochemical phenomena, and the results were rationalized by comparing the obtained data with theoretical models. The effect of this interphase was quantified at a specific welding time and oscillation frequency thanks to rheological modeling. Because of the coupling between rheology and spectroscopical tools, potential reactions between the GMA functions and the amine/carboxylic polyamide chain ends were explored. The results highlighted that the main reaction mechanism was constituted by the crosslinking reaction between the GMA and carboxylic acid units, and not by that between GMA and amine end functions.